Dynamic Pricing and Inventory Management with Regular and Expedited Supplies

We consider a periodic‐review inventory system with regular and expedited supply modes. The expedited supply is faster than the regular supply but incurs a higher cost. Demand for the product in each period is random and sensitive to its selling price. The firm determines its order quantity from each supply in each period as well as its selling price to maximize the expected total discounted profit over a finite or an infinite planning horizon. We show that, in each period if it is optimal to order from both supplies, the optimal inventory policy is determined by two state‐independent thresholds, one for each supply mode, and a list price is set for the product; if only the regular supply is used, the optimal policy is a state‐dependent base‐stock policy, that is, the optimal base‐stock level depends on the starting inventory level, and the optimal selling price is a markdown price that decreases with the starting inventory level. We further study the operational impact of such supply diversification and show that it increases the firm's expected profit, reduces the optimal safety‐stock levels, and lowers the optimal selling price. Thus that diversification is beneficial to both the firm and its customers. Building upon these results, we conduct a numerical study to assess and compare the respective benefit of dynamic pricing and supply diversification.     

Operational Hedging and Diversification under Correlated Supply and Demand Uncertainty

When facing supply uncertainty caused by exogenous factors such as adverse weather conditions, firms diversify their supply sources following the wisdom of “not holding all eggs in one basket.” We study a firm that decides on investment and production levels of two unreliable but substitutable resources. Applying real options thinking, production decisions account for actual supply capabilities, whereas investment decisions are made in advance. To model triangular supply and demand correlations, we adapt the concepts of random capacity and stochastic proportional yield while using concordant ordered random variables. Optimal profit decreases monotonically in supply correlation and increases monotonically in supply–demand correlation. Optimal resource selection, however, depends on the trivariate interplay of supply and demand and responds non‐monotonically to changing correlations. Moreover, supply hedges (i.e., excess capacity at alternative sources) can be optimal even if supply resources are perfectly positively correlated. To accommodate changing degrees of correlation, the firm adjusts the lower margin capacities under random capacity; but under stochastic proportional production capability, it uses either low‐ or high‐margin capacities to create tailored “scale hedges” (i.e., excess capacity at one source which can partially substitute for diversification).     

Managing Retail Shelf and Backroom Inventories When Demand Depends on the Shelf‐Stock Level

Inventory displayed on the retail sales floor not only performs the classical supply function but also plays a role in affecting consumers’ buying behavior and hence the total demand. Empirical evidence from the retail industry shows that for some types of products, higher levels of on‐shelf inventory have a demand‐increasing effect (“billboard effect”) while for some other types of products, higher levels of on‐shelf inventory have a demand‐decreasing effect (“scarcity effect”). This suggests that retailers may use the amount of shelf stock on display as a tool to influence demand and operate a store backroom to hold the inventory of items not displayed on the shelves, introducing the need for efficient management of the backroom and on‐shelf inventories. The purpose of this study is to address such an issue by considering a periodic‐review inventory system in which demand in each period is stochastic and depends on the amount of inventory displayed on the shelf. We first analyze the problem in a finite‐horizon setting and show under a general demand model that the system inventory is optimally replenished by a base‐stock policy and the shelf stock is controlled by two critical points representing the target levels to raise up/drop down the on‐shelf inventory level. In the infinite‐horizon setting, we find that the optimal policies simplify to stationary base‐stock type policies. Under the billboard effect, we further show that the optimal policy is monotone in the system states. Numerical experiments illustrate the value of smart backroom management strategy and show that significant profit gains can be obtained by jointly managing the backroom and on‐shelf inventories.     

Supply Performance in Multi‐Echelon Inventory Systems with Intermediate Product Demand: A Perspective on Allocation

In this article, we study the performance of multi‐echelon inventory systems with intermediate, external product demand in one or more upper echelons. This type of problem is of general interest in inventory theory and of particular importance in supply chain systems with both end‐product demand and spare parts (subassemblies) demand. The multi‐echelon inventory system considered here is a combination of assembly and serial stages with direct demand from more than one node. The aspect of multiple sources of demands leads to interesting inventory allocation problems. The demand and capacity at each node are considered stochastic in nature. A fixed supply and manufacturing lead time is used between the stages. We develop mathematical models for these multi‐echelon systems, which describe the inventory dynamics and allow simulation of the system. A simulation‐based inventory optimization approach is developed to search for the best base‐stock levels for these systems. The gradient estimation technique of perturbation analysis is used to derive sample‐path estimators. We consider four allocation schemes: lexicographic with priority to intermediate demand, lexiographic with priority to downstream demand, predetermined proportional allocation, and proportional allocation. Based on the numerical results we find that no single allocation policy is appropriate under all conditions. Depending on the combinations of variability and utilization we identify conditions under which use of certain allocation polices across the supply chain result in lower costs. Further, we determine how selection of an inappropriate allocation policy in the presence of scarce on‐hand inventory could result in downstream nodes facing acute shortages. Consequently we provide insight on why good allocation policies work well under differing sets of operating conditions.     

Value of and Interaction between Production Postponement and Information Sharing Strategies for Supply Chain Firms

We analyze the value of and interaction between production postponement and information sharing, which are two distinct strategies to reduce manufacturers’ uncertainty about demand. In both single‐level and two‐level supply chains, from the manufacturer's perspective, while information sharing is always valuable, production postponement can sometimes be detrimental. Furthermore, the value of production postponement is not merely driven by savings in inventory holding cost as postponement enables the manufacturer to avoid both excess and shortfall in production. We find that production postponement and information sharing strategies may substitute, complement, or conflict with each other, depending on the extent of the increase in the unit production cost when production is postponed. In a two‐level supply chain, from the retailer's perspective, information sharing and production postponement can be beneficial or detrimental. When information sharing is beneficial to the retailer, the retailer always shares her demand information with the manufacturer voluntarily. In addition, this voluntary information sharing is truthful because inflated or deflated demand information hurts the retailer through a higher wholesale price or a stock‐out. However, the retailer never shares her demand information voluntarily if the manufacturer has already adopted production postponement because production postponement and information sharing strategies always conflict with each other. Even when the retailer does not benefit from information sharing, we show that the manufacturer can always design an incentive mechanism to induce the retailer to share the demand information, irrespective of whether the manufacturer has already implemented production postponement or not. The above findings underscore the need for a careful assessment of demand uncertainty‐reduction strategies before the supply chain players embark upon them.     

Role of Random Capacity Risk and the Retailer in Decentralized Supply Chains with Competing Suppliers

This research considers a supply chain under the following conditions: (i) two heterogeneous suppliers are in competition, (ii) supply capacity is random and pricing is endogenous, (iii) consumer demand, with and without an intermediate retailer, is price dependent. Specifically, we examine how uncertainty in supply capacity affects optimal ordering and pricing decisions, supplier and retailer profits, and the incentives to reduce such uncertainty. When two suppliers sell through a monopolistic retailer, supply uncertainty not only affects the retailer's diversification strategy for replenishment, but also changes the suppliers’ wholesale price competition and the incentive for reducing capacity uncertainty. In this dual‐sourcing model, we show that the benefit of reducing capacity uncertainty depends on the cost heterogeneity between the suppliers. In addition, we show that a supplier does not necessarily benefit from capacity variability reduction. We contrast this incentive misalignment with findings from the single‐supplier case and a supplier‐duopoly case where both suppliers sell directly to market without the monopolistic retailer. In the latter single‐supplier and duopoly cases, we prove that the unreliable supplier always benefits from reducing capacity variability. These results highlight the role of the retailer's diversification strategy in distorting a supplier's incentive for reducing capacity uncertainty under supplier price competition.     

Inventory Management for Customers with Alternative Lead Times

It is common for suppliers operating in batch‐production mode to deal with patient and impatient customers. This paper considers inventory models in which a supplier provides alternative lead times to its customers: a short or a long lead time. Orders from patient customers can be taken by the supplier and included in the next production cycle, while orders from impatient customers have to be satisfied from the on‐hand inventory. We denote the action to commit one unit of on‐hand inventory to patient or impatient customers as the inventory‐commitment decision, and the initial inventory stocking as the inventory‐replenishment decision. We first characterize the optimal inventory‐commitment policy as a threshold type, and then prove that the optimal inventory‐replenishment policy is a base‐stock type. Then, we extend our analysis to models to consider cases of a multi‐cycle setting, a supply‐capacity constraint, and the on‐line charged inventory‐holding cost. We also evaluate and compare the performances of the optimal inventory‐commitment policy and the inventory‐rationing policy. Finally, to further investigate the benefits and pitfalls of introducing an alternative lead‐time choice, we use the customer‐choice model to study the demand gains and losses, known as demand‐induction and demand‐cannibalization effects, respectively.     

Sourcing from Multiple Suppliers for Price‐Dependent Demands

We analyze a model that integrates demand shaping via dynamic pricing and risk mitigation via supply diversification. The firm under consideration replenishes a certain product from a set of capacitated suppliers for a price‐dependent demand in each period. Under deterministic capacities, we derive a multilevel base stock list price policy and establish the optimality of cost‐based supplier selection, that is, ordering from a cheaper source before more expensive ones. With general random capacities, however, neither result holds. While it is optimal to price low for a high inventory level, the optimal order quantities are not monotone with respect to the inventory level. In general, a near reorder‐point policy should be followed. Specifically, there is a reorder point for each supplier such that no order is issued to him when the inventory level is above this point and a positive order is placed almost everywhere when the inventory level is below this point. Under this policy, it may be profitable to order exclusively from the most expensive source. We characterize conditions under which a strict reorder‐point policy and a cost‐based supplier‐selection criterion become optimal. Moreover, we quantify the benefit from dynamic pricing, as opposed to static pricing, and the benefit from multiple sourcing, as opposed to single sourcing. We show that these two strategies exhibit a substitutable relationship. Dynamic pricing is less effective under multiple sourcing than under single sourcing, and supplier diversification is less valuable with price adjustments than without. Under limited supply, dynamic pricing yields a robust, long‐term profit improvement. The value of supply diversification, in contrast, mainly comes from added capacities and is most significant in the short run.     

THE VALUE OF SKU RATIONALIZATION IN PRACTICE (THE POOLING EFFECT UNDER SUBOPTIMAL INVENTORY POLICIES AND NONNORMAL DEMAND)

Several approaches to the widely recognized challenge of managing product variety rely on the pooling effect. Pooling can be accomplished through the reduction of the number of products or stock‐keeping units (SKUs), through postponement of differentiation, or in other ways. These approaches are well known and becoming widely applied in practice. However, theoretical analyses of the pooling effect assume an optimal inventory policy before pooling and after pooling, and, in most cases, that demand is normally distributed. In this article, we address the effect of nonoptimal inventory policies and the effect of nonnormally distributed demand on the value of pooling. First, we show that there is always a range of current inventory levels within which pooling is better and beyond which optimizing inventory policy is better. We also find that the value of pooling may be negative when the inventory policy in use is suboptimal. Second, we use extensive Monte Carlo simulation to examine the value of pooling for nonnormal demand distributions. We find that the value of pooling varies relatively little across the distributions we used, but that it varies considerably with the concentration of uncertainty. We also find that the ranges within which pooling is preferred over optimizing inventory policy generally are quite wide but vary considerably across distributions. Together, this indicates that the value of pooling under an optimal inventory policy is robust across distributions, but that its sensitivity to suboptimal policies is not. Third, we use a set of real (and highly erratic) demand data to analyze the benefits of pooling under optimal and suboptimal policies and nonnormal demand with a high number of SKUs. With our specific but highly nonnormal demand data, we find that pooling is beneficial and robust to suboptimal policies. Altogether, this study provides deeper theoretical, numerical, and empirical understanding of the value of pooling.     

Optimal Dynamic Order Scheduling under Capacity Constraints Given Demand‐Forecast Evolution

We consider a manufacturer without any frozen periods in production schedules so that it can dynamically update the schedules as the demand forecast evolves over time until the realization of actual demand. The manufacturer has a fixed production capacity in each production period, which impacts the time to start production as well as the production schedules. We develop a dynamic optimization model to analyze the optimal production schedules under capacity constraint and demand‐forecast updating. To model the evolution of demand forecasts, we use both additive and multiplicative versions of the martingale model of forecast evolution. We first derive expressions for the optimal base stock levels for a single‐product model. We find that manufacturers located near their market bases can realize most of their potential profits (i.e., profit made when the capacity is unlimited) by building a very limited amount of capacity. For moderate demand uncertainty, we also show that it is almost impossible for manufacturers to compensate for the increase in supply–demand mismatches resulting from long delivery lead times by increasing capacity, making lead‐time reduction a better alternative than capacity expansion. We then extend the model to a multi‐product case and derive expressions for the optimal production quantities for each product given a shared capacity constraint. Using a two‐product model, we show that the manufacturer should utilize its capacity more in earlier periods when the demand for both products is more positively correlated.     

供需不确定条件下基于CVaR的零售商库存鲁棒优化模型

在经典报童模型下考虑供应和需求不确定性,研究了具有风险厌恶的零售商库存优化问题。采用条件风险值（CVaR）对库存绩效进行度量,构建了基于CVaR的零售商库存运作模型;在此基础上,考虑上游供应商供货能力和下游市场需求不确定性,并采用一系列未知概率的离散情景进行描述,给出了供需不确定条件下基于CVaR的零售商库存鲁棒优化模型。进一步,采用区间不确定集对未知情景概率进行建模,给出了基于最大最小准则的鲁棒对应模型。针对同时考虑供需不确定性导致的模型非凸性,采用标准对偶理论将其转化为易于求解的数学规划问题。最后,通过数值计算分析了不同风险厌恶程度和不确定性程度对零售商库存决策以及库存绩效的影响。结果表明,供需不确定性的存在虽然会导致零售商库存绩效损失,但损失值较小。特别地,依据文中模型得到的鲁棒库存策略在多数情况下能够保证零售商获得更优的库存绩效。此外,不确定性和风险厌恶程度的增加虽然会影响零售商库存决策和运作绩效,但在同等风险厌恶态度下,随着不确定性程度的增加,基于文中方法得到的鲁棒库存策略仍能确保零售商获得理想的库存绩效,表明文中所建模型在应对供需不确定性方面具有良好的鲁棒性。     

Demand–Supply Mismatches and Stock Market Performance: A Retailing Perspective

We provide empirical evidence that the volatility of inventory productivity relative to the volatility of demand is a predictor of future stock returns in a sample of publicly listed U.S. retailers over the period 1985–2013. This key performance indicator, entitled demand–supply mismatch (DSM), captures the fact that low variation in inventory productivity relative to variation in demand is indicative of the superior synchronization of demand‐ and supply‐side operations. Applying the Fama and French (1993) three‐factor model augmented with a momentum factor (Carhart 1997), we find that zero‐cost portfolios formed by buying the two lowest and selling the two highest quintiles of DSM stocks yield abnormal stock returns of up to 1.13%. These strong market anomalies related to DSM are observed over the entire sample period and persist after controlling for alternative inventory productivity measures and firm characteristics that are known to predict future stock returns. Further, we reveal that DSM is indicative of lower future earnings and lower sales growth and provide evidence that the observed market inefficiency results from investors’ failure to incorporate all of the information that inventory contains into the pricing of stocks.     

Managing Demand Risk in Tactical Supply Chain Planning for a Global Consumer Electronics Company

We consider the problem of managing demand risk in tactical supply chain planning for a particular global consumer electronics company. The company follows a deterministic replenishment‐and‐planning process despite considerable demand uncertainty. As a possible way to formally address uncertainty, we provide two risk measures, “demand‐at‐risk” (DaR) and “inventory‐at‐risk” (IaR) and two linear programming models to help manage demand uncertainty. The first model is deterministic and can be used to allocate the replenishment schedule from the plants among the customers as per the existing process. The other model is stochastic and can be used to determine the “ideal” replenishment request from the plants under demand uncertainty. The gap between the output of the two models as regards requested replenishment and the values of the risk measures can be used by the company to reallocate capacity among different products and to thus manage demand/inventory risk.     

Dynamic Pricing and Inventory Management with Dual Suppliers of Different Lead Times and Disruption Risks

It is common for a firm to make use of multiple suppliers of different delivery lead times, reliabilities, and costs. In this study, we are concerned with the joint pricing and inventory control problem for such a firm that has a quick‐response supplier and a regular supplier that both suffer random disruptions, and faces price‐sensitive random demands. We aim at characterizing the optimal ordering and pricing policies in each period over a planning horizon, and analyzing the impacts of supply source diversification. We show that, when both suppliers are unreliable, the optimal inventory policy in each period is a reorder point policy and the optimal price is decreasing in the starting inventory level in that period. In addition, we show that having supply source diversification or higher supplier reliability increases the firm's optimal profit and lowers the optimal selling price. We also demonstrate that, with the selling price as a decision, a supplier may receive even more orders from the firm after an additional supplier is introduced. For the special case where the quick‐response supplier is perfectly reliable, we further show that the optimal inventory policy is of a base‐stock type and the optimal pricing policy is a list‐price policy with markdowns.     

Centralization versus decentralization: Risk pooling,risk diversification,and supply chain disruptions

We investigate optimal system design in a multi-location system in which supply is subject to disruptions. We examine the expected costs and cost variances of the system in both a centralized and a decentralized inventory system. We show that, when demand is deterministic and supply may be disrupted, using a decentralized inventory design reduces cost variance through the risk diversification effect, and therefore a decentralized inventory system is optimal. This is in contrast to the classical result that when supply is deterministic and demand is stochastic, centralization is optimal due to the risk-pooling effect. When both supply may be disrupted and demand is stochastic, we demonstrate that a risk-averse firm should typically choose a decentralized inventory system design.     

Promotion Planning and Supply Chain Contracting in a High–Low Pricing Environment

Demand forecast errors threaten the profitability of high–low price promotion strategies. This article shows how to match demand and supply effectively by means of two‐segment demand forecasting and supply contracts. We find that demand depends on the path of past retail prices, which leads to only a limited number of reachable demand states. However, forecast errors cannot be entirely eliminated because competitive promotions entail some degree of random (i.e., last‐minute) pricing. A hedging approach can be deployed to distribute demand risk efficiently over multiple promotional campaigns and within the supply chain. A retailer that employs a portfolio of forward, option, and spot contracts can avoid both stockouts and excess inventories while achieving the first‐best solution and Pareto improvements. We provide an improved forecasting method as well as stochastic programs to solve for optimal production and purchasing policies such that the right amount of inventory is available at the right time. By connecting a stockpiling model of demand with the supply side, we derive insights on optimal risk management strategies for both manufacturers and retailers in a market environment characterized by frequent price promotions and multiple discount levels. We employ a data set of the German retail market for a key generator of store traffic—namely, diapers.     

Dynamic Supply Risk Management with Signal‐Based Forecast,Multi‐Sourcing,and Discretionary Selling

We examine the critical role of advance supply signals—such as suppliers’ financial health and production viability—in dynamic supply risk management. The firm operates an inventory system with multiple demand classes and multiple suppliers. The sales are discretionary and the suppliers are susceptible to both systematic and operational risks. We develop a hierarchical Markov model that captures the essential features of advance supply signals, and integrate it with procurement and selling decisions. We characterize the optimal procurement and selling policy, and the strategic relationship between signal‐based forecast, multi‐sourcing, and discretionary selling. We show that higher demand heterogeneity may reduce the value of discretionary selling, and that the mean value‐based forecast may outperform the stationary distribution‐based forecast. This work advances our understanding on when and how to use advance supply signals in dynamic risk management. Future supply risk erodes profitability but enhances the marginal value of current inventory. A signal of future supply shortage raises both base stock and demand rationing levels, thereby boosting the current production and tightening the current sales. Signal‐based dynamic forecast effectively guides the firm's procurement and selling decisions. Its value critically depends on supply volatility and scarcity. Ignoring advance supply signals can result in misleading recommendations and severe losses. Signal‐based dynamic supply forecast should be used when: (a) supply uncertainty is substantial, (b) supply‐demand ratio is moderate, (c) forecast precision is high, and (d) supplier heterogeneity is high.     

Managing Supply Risk for Vertically Differentiated Co‐Products

The manufacturing complexity of many high‐tech products results in a substantial variation in the quality of the units produced. After manufacturing, the units are classified into vertically differentiated products. These products are typically obtained in uncontrollable fractions, leading to mismatches between their demand and supply. We focus on product stockouts due to the supply–demand mismatches. Existing literature suggests that when faced with product stockouts, firms should satisfy all unmet demand of a low‐end product by downgrading excess units of a high‐end product (downward substitution). However, this policy may be suboptimal if it is likely that low‐end customers will substitute with a higher quality product and pay the higher price (upward substitution). In this study, we investigate whether and how much downward substitution firms should perform. We also investigate whether and how much low‐end inventory firms should withhold to strategically divert some low‐end demand to the high‐end product. We first establish the existence of regions of co‐production technology and willingness of customers to substitute upward where firms adopt different substitution/withholding strategies. Then, we develop a managerial framework to determine the optimal selling strategy during the life cycle of technology products as profit margins shrink, manufacturing technology improves, and more capacity becomes available. Consistent trends exist for exogenous and endogenous prices.     

BlueLinx can benefit from innovative inventory management methods for commodity forward buys

Commodity prices often fluctuate significantly from one purchasing opportunity to the next. These fluctuations allow firms to benefit from forward buying (buying for future demand in addition to current demand) when prices are low. We propose a combined heuristic to determine the optimal number of future periods a firm should purchase at each ordering opportunity in order to maximize total expected profit when there is uncertainty in future demand and future buying price. We compare our heuristic with existing methods via simulation using real demand data from BlueLinx, a two-stage distributor of building products. The results show that our combined heuristic performs better than any existing methods considering forward buying or safety stock separately. We also compare our heuristic to the optimal inventory management policy by full enumeration for a smaller data set. The proposed heuristic is shown to be close to optimal. This study is the first to decide both the optimal number of future periods to buy for uncertain purchase price and the appropriate purchasing quantity with safety stock for uncertain demand simultaneously. The experience suggests that the proposed combined heuristic is simple and can be very beneficial for any company where forward buying is possible.     

Addressing Supply–Demand Imbalance: Designing Efficient Remanufacturing Strategies

The management of remanufacturing inventory system is often challenged by mismatched supply (i.e., returned units, called cores) and demand. Typically, the demand for remanufactured units is high and exceeds the supply early in a product's lifetime, and drops below the supply late in the lifetime. This supply–demand imbalance motivates us to study a switching strategy to facilitate the decision‐making process. This strategy deploys a push mode at the early stage of a product's lifetime, which remanufactures scarce cores to stock to responsively satisfy the high demand, and switches to a pull mode as the product approaches obsolescence to accurately match the low demand with supply. In addition, the strategy further simplifies the decision‐making process by ignoring the impact of leftover cores at the end of each decision period. We show that the optimal policy of the switching strategy possesses a simple, multi‐dimensional base‐stock structure, which aims to remanufacture units from the i best‐quality categories up to the ith state‐independent base‐stock level. An extensive numerical study shows that the switching strategy delivers close‐to‐optimal and robust performance: the strategy only incurs an average profit loss of 1.21% and a maximum of 2.27%, compared with the optimal one. The numerical study also shows when a pure push or pull strategy, a special case of the switching strategy, delivers good performance. The study offers the managerial insight that firms can use simple, easy‐to‐implement strategies to efficiently manage the remanufacturing inventory system.